Note that, in Corollary REF  as we require \(t\in (0,t(N)]\)  and \(t(N)=\mathcal {O}(\log (N))\)  this may not be as useful as Corollary REF , but the assumption of a stable system in Corollary REF  is much stronger than the hypotheses in Corollary REF ; see [1]} for a discussion.
